Question: Find an ordered pair $(u,v)$ that solves the system: \begin{align*} 5u &= -7 - 2v,\\ 3u &= 4v - 25 \end{align*}
Explanation: Multiplying the first equation by $2$ gives $10u = -14 - 4v$.  Adding this to the second equation gives $13u = -39$, so $ u= -3$.  Substituting this into $5u=-7-2v$ gives $-15=-7-2v$, so $v = 4$ and our solution is $(u,v) =\boxed{(-3,4)}$.